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Advertive topological algebras. (English) Zbl 1044.46038
Abel, Mati (ed.), General topological algebras. Proceedings of the international workshop, Tartu, Estonia, October 4–7, 1999. Tartu: Estonian Mathematical Society (ISBN 9985-9235-6-1/pbk). Math. Stud., Tartu 1, 14-24 (2001).
Let $$A$$ be a topological algebra with separately continuous multiplication. The topological radical rad $$A$$ of a topological algebra $$A$$ has been defined and studied by the author in [Math. Stud., Tartu 1, 25–31 (2001; Zbl 1044.46039), see the following review]. $$A$$ is an advertive topological algebra if the set of topologically quasi-invertible elements of $$A$$ coincides with the set of quasi-invertible elements of $$A$$. The class of advertive algebras contains all Q-algebras, all complete locally $$m$$-pseudoconvex algebras, and all topological algebras with functional spectrum. If $$A$$ is a commutative topologically nonradical simplicial Gelfand-Mazur algebra, then the set hom $$A$$ is not empty. If $$A$$ is a Hausdorff complex algebra and if completion of $$A$$ is a Q-algebra, then the classes of topological Q-algebras, advertive topological algebras, and advertible complete algebras coincide.
For the entire collection see [Zbl 0969.00059].

##### MSC:
 46H05 General theory of topological algebras 46H20 Structure, classification of topological algebras